PSI - Issue 41

Daniele Gaetano et al. / Procedia Structural Integrity 41 (2022) 439–451 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The nonlinear behavior of the given composite beam has been extracted by means of the proposed multiscale approach, after defining a proper Repeating Unit Cell (RUC), which is depicted in Fig. 3b. According to the three different operational steps reported in Section 2.2, the following computations have been performed. Firstly, the nine components of the undamaged in-plane moduli tensor have been computed, by means of a classical linear homogenization step, involving three macro-strain paths, i.e., two uniaxial and a shear path. Secondly, the nonlinear homogenized response of the microstructure has been derived, in terms of macro-stress 11 M  vs macro-strain 11 M  curve along the horizontal uniaxial macro-strain path direction, inducing a pure Mode-I macro-crack propagation, as depicted in Fig. 4a. After this, the complete damaged moduli tensor has been derived by assuming an isotropic macroscopic damage evolution function   11 M M M d d   , which is directly extracted from the homogenized uniaxial stress-strain curve obtained from the principal path solution imposed on the RUC, as shown in Fig. 4b. Finally, a pure Mode-I homogenized traction-separation law,   coh coh , , , M n M n M n t t u    , n denoting the normal component of the relevant vectors, is extracted from the previously derived uniaxial stress-strain relation, as shown in Fig. 5a. This law is properly split in a purely hardening and softening portion, by virtue of the energy-based procedure presented in Section 2.1, so that a localized traction-separation law is extracted (see Fig. 5b).

Fig. 4. Numerical outcomes of the nonlinear bulk homogenization step: (a) homogenized uniaxial respone of the Repeating Unit Cell; (b) homogenized damage evolution function.

Fig. 5. Numerical outcomes of the nonlinear interface homogenization step: (a) total homogenized traction-separation law; (b) localized homogenized traction-separation law.